Multipliers for p-Bessel sequences in Banach spaces

Multipliers have been recently introduced as operators for Bessel sequences and frames in Hilbert spaces. These operators are defined by a fixed multiplication pattern (the symbol) which is inserted between the analysis and synthesis operators. In this paper, we will generalize the concept of Bessel multipliers for p-Bessel and p-Riesz sequences in Banach spaces. It will be shown that bounded symbols lead to bounded operators. Symbols converging to zero induce compact operators. Furthermore, we will give sufficient conditions for multipliers to be nuclear operators. Finally, we will show the continuous dependency of the multipliers on their parameters.Comment: 17 page

The Four Phases of Philosophy

Introduction and translation of “The Four Phases of Philosophy” by Franz Brentano

Diet of oceanic loggerhead sea turtles (Caretta caretta) in the central North Pacific

Diet analysis of 52 loggerhead sea turtles (Caretta caretta) collected as bycatch from 1990 to 1992 in the high-seas driftnet fishery operating between lat. 29.5°N and 43°N and between long. 150°E and 154°W demonstrated that these turtles fed predominately at the surface; few deeper water prey items were present in their stomachs. The turtles ranged in size from 13.5 to 74.0 cm curved carapace length. Whole turtles (n =10) and excised stomachs (n= 42) were frozen and transported to a laboratory for analysis of major faunal components. Neustonic species accounted for four of the five most common prey taxa. The most common prey items were Janthina spp. (Gastropoda); Carinaria cithara Benson 1835 (Heteropoda); a chondrophore, Velella velella (Hydrodia); Lepas spp. (Cirripedia), Planes spp. (Decapoda: Grapsidae), and pyrosomas (Pyrosoma spp.)

Scaling gridded river networks for macroscale hydrology: Development, analysis, and control of error

A simple and robust river network scaling algorithm (NSA) is presented to rescale fine‐resolution networks to any coarser resolution. The algorithm was tested over the Danube River basin and the European continent. Coarse‐resolution networks, at 2.5, 5, 10, and 30 min resolutions, were derived from higher‐resolution gridded networks using NSA and geomorphometric attributes, such as river order, shape index, and width function. These parameters were calculated and compared at each resolution. Simple scaling relationships were found to predict decreasing river lengths with coarser‐resolution data. This relationship can be used to correct river length as a function of grid resolution. The length‐corrected width functions of the major river basins in Europe were compared at different resolutions to assess river network performance. The discretization error in representing basin area and river lengths at coarser resolutions were analyzed, and simple relationships were found to calculate the minimum number of grid cells needed to maintain the catchment area and length within a desired level of accuracy. This relationship among geomorphological characteristics, such as shape index and width function (derived from gridded networks at different resolutions), suggests that a minimum of 200–300 grid cells is necessary to maintain the geomorphological characteristics of the river networks with sufficient accuracy

Optimal one-dimensional coverage by unreliable sensors

This paper regards the problem of optimally placing unreliable sensors in a one-dimensional environment. We assume that sensors can fail with a certain probability and we minimize the expected maximum distance from any point in the environment to the closest active sensor. We provide a computational method to find the optimal placement and we estimate the relative quality of equispaced and random placements. We prove that the former is asymptotically equivalent to the optimal placement when the number of sensors goes to infinity, with a cost ratio converging to 1, while the cost of the latter remains strictly larger.Comment: 21 pages 2 figure

Global system of rivers: Its role in organizing continental land mass and defining land‐to‐ocean linkages

The spatial organization of the Earth\u27s land mass is analyzed using a simulated topological network (STN‐30p) representing potential flow pathways across the entire nonglacierized surface of the globe at 30‐min (longitude × latitude) spatial resolution. We discuss a semiautomated procedure to develop this topology combining digital elevation models and manual network editing. STN‐30p was verified against several independent sources including map products and drainage basin statistics, although we found substantial inconsistency within the extant literature itself. A broad suite of diagnostics is offered that quantitatively describes individual grid cells, river segments, and complete drainage systems spanning orders 1 through 6 based on the Strahler classification scheme. Continental and global‐scale summaries of key STN‐30p attributes are given. Summaries are also presented which distinguish basins that potentially deliver discharge to an ocean (exorheic) from those that potentially empty into an internal receiving body (endorheic). A total of 59,122 individual grid cells constitutes the global nonglacierized land mass. At 30‐min spatial resolution, the cells are organized into 33,251 distinct river segments which define 6152 drainage basins. A global total of 133.1 × 106 km2 bear STN‐SOp flow paths with a total length of 3.24 × 106 km. The organization of river networks has an important role in linking land mass to ocean. From a continental perspective, low‐order river segments (orders 1‐3) drain the largest fraction of land (90%) and thus constitute a primary source area for runoff and constituents. From an oceanic perspective, however, the small number (n=101) of large drainage systems (orders 4‐6) predominates; draining 65% of global land area and subsuming a large fraction of the otherwise spatially remote low‐order rivers. Along river corridors, only 10% of land mass is within 100 km of a coastline, 25% is within 250 km, and 50% is within 750 km. The global mean distance to river mouth is 1050 km with individual continental values from 460 to 1340 km. The Mediterranean/Black Sea and Arctic Ocean are the most land‐dominated of all oceans with land:ocean area ratios of 4.4 and 1.2, respectively; remaining oceans show ratios from 0.55 to 0.13. We discuss limitations of the STN‐30p together with its potential role in future global change studies. STN‐30p is geographically linked to several hundred river discharge and chemistry monitoring stations to provide a framework for calibrating and validating macroscale hydrology and biogeochemical flux models

Discrete coherent states for higher Landau levels

We consider the quantum dynamics of a charged particle evolving under the action of a constant homogeneous magnetic field, with emphasis on the discrete subgroups of the Heisenberg group (in the Euclidean case) and of the SL(2, R) group (in the Hyperbolic case). We investigate completeness properties of discrete coherent states associated with higher order Euclidean and hyperbolic Landau levels, partially extending classic results of Perelomov and of Bargmann, Butera, Girardello and Klauder. In the Euclidean case, our results follow from identifying the completeness problem with known results from the theory of Gabor frames. The results for the hyperbolic setting follow by using a combination of methods from coherent states, time-scale analysis and the theory of Fuchsian groups and their associated automorphic forms.Comment: Revised for Annals of Physic

A Comparison of Predictions for SM Higgs Boson Production at the LHC

This paper describes a comparison of most of the available predictions for the cross section and transverse momentum distribution for a 125 GeV mass Higgs at the LHC, including those from the PYTHIA and HERWIG parton shower Monte Carlos and from four resummation calculations.Comment: 7 pages, submitted to proceedings of the Workshop on Physics at TeV Colliders, Les Houches 200